Reduced complexity coding system using iterative decoding

ABSTRACT

A concatenated coding scheme, using an outer coder, interleaver, and the inner coder inherent in an FQPSK signal to form a coded FQPSK signal. The inner coder is modified to enable interactive decoding of the outer code.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional Application60/285,903, filed Apr. 23, 2001.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under grant no.NAS7-1407. The government may have certain rights in this invention.

Properties of a channel affect the amount of data that can be handled bythe channel. The so-called “Shannon limit” defines the theoretical limitof amount of data that a channel can carry.

Different techniques have been used to increase the data rate that canbe handled by a channel. “Near Shannon Limit Error-Correcting Coding andDecoding: Turbo Codes,” by Berrou et al. ICC, pp 1064-1070, (1993),described a new “turbo code” technique that has revolutionized the fieldof error correcting codes.

Turbo codes have sufficient randomness to allow reliable communicationover the channel at a high data rate near capacity. However, they stillretain sufficient structure to allow practical encoding and decodingalgorithms.

Feher's patented QPSK, or FQPSK, as described in detail in U.S. Pat.Nos. 4,567,602; 4,339,724; 4,644,565; 5,784,402; and 5,491,457 is acoded modulation scheme. The generic form of FQPSK is based oncrosscorrelated phase-shift-keying. FQPSK maintains a nearly constantenvelope, that is the maximum fluctuation in the envelope is around 0.18dB. This is done by manipulating the pulse shapes of the in-phase “I”and quadrature “Q” signals using crosscorrelation mapping.

Many different variants of FQPSK are known, including FQPSK-B, which isa bandwidth limited form of FQPSK.

The price of this spectral efficiency of these coded modulation schemesmay be a degradation in the bit error rate performance.

SUMMARY OF THE INVENTION

The present application teaches a new technique which allows additionalpower efficiency and bandwidth efficiency with a simple receiverarchitecture. This technique may use turbo coding techniques, along witha specially configured FQPSK encoder and/or decoder, to form aconcatenated coded modulation scheme.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects will now be described in detail with referenceto the accompanying drawings, wherein:

FIG. 1 shows a conceptual diagram of FQPSK;

FIG. 2 shows an alternative implementation of the baseband signals usingmapping;

FIG. 3 shows full symbol waveforms of FQPSK;

FIG. 4 shows a trellis decoding interpretation used for a receiver;

FIG. 5 shows a bit error rate comparison of the different techniques;

FIG. 6 shows averaged waveforms for the simplified receiver;

FIG. 7 shows at trellis diagram for the simplified receiver;

FIG. 8 shows a simplified implementation of the baseband signals;

FIG. 9 shows a simplified receiver;

FIGS. 10 a-b show original and remapped encoders and trellises for thereceiver to be used in concatenated schemes;

FIGS. 11-13 show embodiments of the improved transmitter and receiver;and

FIG. 14 shows a soft input soft output outer decoder for a rate ½repetition outer code.

DETAILED DESCRIPTION

FQPSK in its standard form is similar to many phase-shift-keyingtechniques which had been previously used. A conceptual diagram of FQPSKis shown in FIG. 1. One advantage of the specific FQPSK system is a 3 dbenvelope reduction based on intentional but controlled crosscorrelationbetween the I and Q channels. This was described by half symbol mappingsof the 16 possible combinations of I and Q channel waveforms that werepresent in the signal, into a specified set of 16 waveform combinations.These 16 waveform combinations were selected in a way that rendered thecrosscorrelated output time continuous. The waveform combinations alsohad unit, normalized, envelopes at each of the I and Q uniform samplinginstants.

Since the crosscorrelation mapping was based on half symbolcharacterization of the signal, there was no guarantee that the slope ofthe crosscorrelated output waveform would be continuous at thetransitions between the half symbol points. In fact, a slopediscontinuity may occur statistically one-quarter of the time.

In a copending patent application, it is suggested to structure thecrosscorrelation mapping into a full symbol by symbol mapping, ratherthan a half symbol by half symbol representation. In fact, thistechnique also has the advantage of enabling data transitions on the Iand Q channels to be described directly. Moreover, this enables areceiver for FQPSK which exploits the specific correlation (memory) thatis introduced into the modulation scheme.

FIG. 2 illustrates the interpretation of FQPSK as a trellis-codedmodulation. The input streams of data bits are split into time-aligned Iand Q symbol streams at half the usual bit rate, so 1/T_(s)=½T_(b). Eachof these symbol streams is passed through specific rate ⅓ encoders. Therate ⅓ encoder 200 for the I stream 200 is different than the rate ⅓encoder 240 for the Q stream 250. The output bits of these encoders arethen considered to be grouped into one of three different categories.

The three categories include a first category of bits that onlyinfluence the choice of the signal in the same channel. A secondcategory of bits only influence the choice of the signal in the otherchannel. A third category of bits influence choices of signals in bothchannels, that is represent crosscorrelation mapping.

Out of the bit sequences from the I encoder 200, the value I3 signal 201is used to determine the signal that is transmitted on the I channel.The value Q0 signal 202, is used to determine the signal transmitted onthe Q channel. The value I2, which is the same as Q1, signal 203, isused to determine both the signals transmitted on I and Q channels.

If d_(1n) and d_(Qn) respectively denote the +1 and −1 I and Q datasymbols in the nth transmission interval and

$D_{l\; n}\overset{\Delta}{=}{{{\left( {1 - d_{l\; n}} \right)/2}\mspace{14mu}{and}\mspace{14mu} D_{Qn}}\overset{\Delta}{=}{\left( {1 - d_{Qn}} \right)/2}}$their (0, 1) equivalents, then the mappings appropriate to the I and Qencoders of FIG. 2 areI ₀ =D _(Qn) ⊕D _(Q,n−1) , Q ₀ =D _(l,n+1) ⊕D _(ln)I ₁ =D _(Q,n−1) ⊕D _(Q,n−2) , Q ₁ =D _(ln) ⊕D _(I,n−1) =I ₂I ₂ =D _(ln) ⊕D _(I,n−1) , Q ₂ =D _(Qn) ⊕D _(Q,n−1) =I ₀I ₃ =D _(ln) , Q ₃ =D _(Qn)  (1)These values correspond to the four, I channel coded bits which includetwo from the I encoder output and two from the Q encoder output.Analogously, it includes four, Q channel encoded bits.

The values i,j are used as binary coded decimal indices defined asfollows:i=I ₃×2³ +I ₂×2² +I ₁×2¹ ×I ₀×2⁰j=Q ₃×2³ +Q ₂×2² +Q ₁×2¹ +Q ₀×2⁰  (2)

The indices i and j may range between zero and 15. A set of basebandsignals are shown in FIG. 3. These symbols may be defined as

$\begin{matrix}\begin{matrix}{{s_{1}(t)} = \left\{ {\begin{matrix}{A,} & {{{- T_{s}}/2} \leq t \leq 0} \\{{1 - {\left( {1 - A} \right)\cos^{2}\pi\;\frac{t}{T_{s}}}},} & {0 \leq t \leq {T_{s}/2}}\end{matrix},{{s_{9}(t)} = {- {s_{1}(t)}}}} \right.} \\{{s_{2}(t)} = \left\{ {\begin{matrix}{{1 - {\left( {1 - A} \right)\cos^{2}\pi\;\frac{t}{T_{s}}}},} & {{{- T_{s}}/2} \leq t \leq 0} \\{A,} & {0 \leq t \leq {T_{s}/2}}\end{matrix},{{s_{10}(t)} = {- {s_{2}(t)}}}} \right.} \\{{{s_{3}(t)} = {1 - {\left( {1 - A} \right)\cos^{2}\pi\;\frac{t}{T_{s}}}}},{{{{- T_{s}}/2} \leq t \leq {{T_{s}/2}\mspace{20mu}{s_{11}(t)}}} = {- {s_{3}(t)}}}} \\{{{s_{4}(t)} = {A\;\sin\pi\;\frac{t}{T_{s}}}},{{{- T_{s}}/2} \leq t \leq {T_{s}/2}},{{s_{12}(t)} = {- {s_{4}(t)}}}} \\{{s_{5}(t)} = \left\{ {\begin{matrix}{{A\;\sin\pi\;\frac{t}{T_{s}}},} & {{{- T_{s}}/2} \leq t \leq 0} \\{{\sin\pi\;\frac{t}{T_{s}}},} & {0 \leq t \leq {T_{s}/2}}\end{matrix},{{s_{13}(t)} = {- {s_{5}(t)}}}} \right.} \\{{s_{6}(t)} = \left\{ {\begin{matrix}{{\sin\pi\;\frac{t}{T_{s}}},} & {{{- T_{s}}/2} \leq t \leq 0} \\{{A\;\sin\pi\;\frac{t}{T_{s}}},} & {0 \leq t \leq {T_{s}/2}}\end{matrix},{{s_{14}(t)} = {- {s_{6}(t)}}}} \right.} \\{{{s_{7}(t)} = {\sin\pi\;\frac{t}{T_{s}}}},{{{- T_{s}}/2} \leq t \leq {T_{s}/2}},{{s_{15}(t)} = {- {s_{7}(t)}}}}\end{matrix} & (3)\end{matrix}$

The pair of indices are used to select which of these baseband signalss_(i)(t), s_(j)(t) will be transmitted respectively over the I and Qchannels in any symbol interval.

For any value of A other than unity, certain waveforms will have adiscontinuous slope at their midpoints (T=0). For example, it has beensuggested that A should equal 1/sqrt(2) to produce minimum envelopefluctuation. When that happens, the waveforms 5 and 6 as well as theirnegatives 13 and 14, will have a discontinuous slope at those midpoints.

Finally, the I and Q baseband signals s_(i)(t) and s_(q)(t) are offsetby half a symbol relative to one another, and modulated onto thequadrature channels for transmission.

This trellis-coded characterization of FQPSK is, in principal, an M-arysignaling scheme. This means that a given pair of I and Q data symbolsresults in the transmission of a given pair of I and Q waveforms in eachsignaling interval. Restrictions are placed on the allowable sequencesof waveforms that can be transmitted in either of these channels toproduce continuous I and Q waveform sequences. The present inventorsnoticed that these restrictions on the transitional behavior of thetransmitted signal results in the narrow spectrum characteristic ofFQPSK. The inventors also noticed that the trellis coded structure ofthe transmitter suggests that an optimum receiver for FQPSK should be aform of trellis demodulator. It has been suggested to use of bank of 16biased matched filters followed by a 16 state trellis demodulator. Thisconfiguration is shown in FIG. 4. The simulated bit error rateperformance of this receiver is shown in FIG. 5 and compared with aconventional receiver as well as the performance of conventional uncodedQPSK.

This receiver may be relatively complex, and hence simplifiedconfigurations may be desirable. An averaged matched filter that ismatched to the average of the 16 waveforms may replace the bank of 16matched filters. A reduced complexity of the Viterbi receiver recognizessimilarities in shape properties of certain members of the waveforms,and separates them into different groups. The waveforms s0-s3 aregrouped as a first, composite waveform, with each four waveforms beingsimilarly grouped as follows:

$\begin{matrix}\begin{matrix}{{{q_{0}(t)} = {\sum\limits_{i = 0}^{3}\;{s_{i}(t)}}},} & {{{q_{1}(t)} = {\sum\limits_{i = 4}^{7}\;{s_{i}(t)}}},} \\{{{q_{2}(t)} = {{\sum\limits_{i = 8}^{11}\;{s_{i}(t)}} = {- {q_{0}(t)}}}},} & {{q_{3}(t)} = {{\sum\limits_{i = 12}^{15}\;{s_{i}(t)}} = {- {q_{1}(t)}}}}\end{matrix} & (4)\end{matrix}$

The waveform assignments of the group members are then replaced by theircorresponding average waveform that is, any of s0 to s3 become q0 to q3.This causes the crosscorrelation between the I and Q channels toeffectively disappear. Effectively, the I channel signal is selectedbased on only the I encoder output bits, and the Q channel signal isbased on only the Q encoder output bits. When this happens, then thetrellis coded structure decouples into two independent I and Q two statetrellises; see FIG. 7. The transmitter simplifies into the FIG. 8structure with a corresponding optimum receiver being shown in FIG. 9.The I and Q decisions are no longer produced jointly, but rather areproduced separately by individual Viterbi techniques acting on energybased correlations from the I and Q modulated signals. The degradationin bit error rate relative to the optimum receiver may be compensated bythe significant reduction in complexity of the receiver.

FQPSK, as described above is a convolutional coded modulation. It isrecognized by the inventors that a potentially large coding gain may beachievable using iterative/recursive encoding and decoding ofconcatenated codes with a soft input soft output a posterioriprobability algorithm.

The techniques of concatenated codes are well-known. In general, thissystem has two encoders: an outer coder and an inner coder separated byan interleaver. A serial concatenated code operates serially, while aparallel concatenated code operates in parallel. An outer encoderreceives the uncoded data. The outer coder can be an (n,k) binary linearencoder where n>k. The means that the encoder 200 accepts as input ablock u of k data bits. It produces an output block v of n data bits. Inits simplest form, the outer coder may be a repetition coder. The outercoder codes data with a rate that is less than 1, and may be, forexample, ½ or ⅓.

The interleaver 220 performs a fixed pseudo-random permutation of theblock v, yielding a block w having the same length as v. The permutationcan be an identity matrix, where the output becomes identically the sameas the input. Alternately and more preferably, the permutationrearranges the bits in a specified way.

The inner encoder 210 is a linear rate 1 encoder.

According to a present system, this technique is applied to FQPSK. It isrecognized that the inherent coding that is carried out in FQPSK maysupply the inner code for the iterative concatenated code. In theembodiments, the outer coded signal is applied to a FQPSK system whichmay use the simplified receiver of FIG. 9. The two state Viterbialgorithms are replaced with two state soft input-soft output (SISO)Max-log algorithms as described in the literature. These may beconsidered as modified soft output Viterbi algorithms. Aninterleaving/deinterleaving process is applied between the inner andouter codes. A coding gain from this interleaving process can beobtained by remapping the I and Q FQPSK inner codes from nonrecursiveinto recursive type codes, using other known techniques. FIGS. 10 a-10 bshow the original I and Q encoders and the remapped I and Q encoders forthis purpose.

This remapping provides recursiveness for the parts of the FQPSKencoders that are matched to the reduced two state soft input-softoutput decoder for the inner code.

The remapped encoders would produce different baseband waveforms.However, the allowable FQPSK encoder output sequences would remain thesame. Therefore, both the envelope and spectral characteristics of themodulated signal would be identical to those produced by the FQPSKsignal in the transmitter in FIG. 2.

When an outer code is added, an interleaver is used which has a sizethat is large enough to approximately output an uncorrelated sequence.

FIGS. 11-13 shows three different embodiments of applying an outer codeto the FQPSK modulator/demodulator using a concatenated system withiterative decoding. A number N of input bits 1100 are applied to ademultiplexer 1105 that divides the bits between a pair of outerencoders 1110, 1115 of rate R. These effectively form the I and Qchannel bit streams. Each of the outer-encoded bits are applied tointerleavers 1120, 1121. The I and Q channels are then applied to aFQPSK inner code modulator 1125 which forms the inner code of such asystem. The thus coded stream 1130 is transmitted over the channel 1135.The receiver included a matched filter bank 111 with biases, thatproduces I and Q output channels. Each of those channels goes through asoft input-soft output FQPSK demodulator 1145,1146 whose output iscoupled to a deinterleaver 1150,1151. After passing through decisionunits 1160 and 1161, the resulting I and Q baseband signals aremultiplexed in 1165 to provide the decoded output bits 1170.

In this and the other similar embodiments, the energy biased matchedfilter bank 1140 provides for branch metrics per I and Q channel for thesimplified, two state soft in soft out FQPSK coders. The decoders1145,1146 provide extrinsics associated with the FQPSK encoder inputbits to the outer coder via the deinterleavers 1150, 1151. These areapplied to the outer decoders 1155,1156 to provide new versions of thereceived extrinsics by using the code constraint as an output extrinsicthrough the interleavers. The other outputs are fed back to the inputsof the demodulators 1145,1146.

In operation, the process may repeat/iterate several times. At the endof the final iteration, the output of the outer decoders 1155, 1156 arehard limited in order to produce decisions on the bits.

An alternative system shown in FIG. 12 receives the input bits 1100directly to an outer encoder 1205, and interleaver 1210 whose output isdemultiplexed by 1215 and applied to the FQPSK inner code modulator1220. This system may use an analogous receiver with the matched filterbank 1140, applied to similar demodulators 1145, 1146. The demodulatedoutputs are multiplexed by 1250, and deinterleaved 1255, and then outerdecoded 1260. The feedback loop in this system uses an interleaver 1265and demultiplexer 1270 to provide the I and Q channels.

FIG. 13 shows a parallel concatenated coding system, in which a rate 1outer encoder is formed from the input bitstream and the interleavedinput bitstream and the interleaved input bitstream as in a turbo code.The input bits 1300 are split with one set of bits being interleaved by1305. The input bits and interleaved input bits are applied in parallelto the inner coder/FQPSK module 1310 which outputs a coded bitstream1315 that is applied to the channel 1320. Data from the channel isreceived into a matched filter bank type receiver 1325 that iterativelycalculates the output.

The outer coder may simply be a rate ½ repetition outer coder, with ablock interleaver of size n. The outer decoder 1155 may be significantlysimplified for the repetition code. For this code, the outer decoder maysimply swap the order of successive pairs of bits as shown in FIG. 14.

Computer simulations of this system show an improvement of 3.75 dB at upbit error rate of 10⁻⁵.

Although only a few embodiments have been disclosed in detail above,other modifications are possible. All such modifications are intended tobeing comps within the following claims, in which:

1. A method of encoding, comprising: performing a first outer encodingon a first portion of an input sequence of bits to produce first outerencoded bits; performing a second outer encoding on a second portion ofthe input sequence of bits to produce second outer encoded bits; bitinterleaving said first outer encoded bits to produce first interleavedencoded bits; bit interleaving said second outer encoded bits to producesecond interleaved encoded bits; performing a modified FQPSK modulationon said first interleaved encoded bits and said second interleavedencoded bits to produce I and Q waveform sequences, wherein saidperforming the modified FQPSK modulation realizes a modulation withmemory, wherein said performing the modified FQPSK modulation includes:performing an I-channel recursive encoding on the first interleavedencoded bits to generate I encoder outputs; performing a Q-channelrecursive encoding on the second interleaved encoded bits to generate Qencoder outputs; performing a signal mapping on the I encoder outputsand the Q encoder outputs to generate said I and Q waveform sequences;wherein said I and Q waveform sequences are continuous in time.
 2. Themethod of claim 1, wherein said performing the signal mapping generatesthe I waveform sequence based on the I encoder outputs and generates theQ waveform sequence based on the Q encoder outputs.
 3. The method ofclaim 1, wherein said first and second outer encodings are linearencodings each with rate less than one.
 4. The method of claim 1,wherein said first and second outer encodings are each repetitionencodings.
 5. The method of claim 1, wherein said performing themodified FQPSK modulation also includes: performing quadraturemodulation on quadrature carrier signals using respectively the I and Qwaveform sequences to generate an output signal.
 6. The method of claim1 further comprising transmitting an output signal onto a channel,wherein the output signal is determined using the I and Q waveformsequences.
 7. A method of encoding, comprising: outer encoding an inputsequence of bits to produce outer encoded bits; bit interleaving saidouter encoded bits to produce interleaved encoded bits; and performing amodified FQPSK modulation on said interleaved encoded bits to produce Iand Q waveform sequences, wherein said performing the modified FQPSKmodulation realizes a modulation with memory, wherein said performingthe modified FQPSK modulation includes: performing an I-channelrecursive encoding on a first portion of said interleaved encoded bitsto generate I encoder outputs; performing a Q-channel recursive encodingon a second portion of said interleaved encoded bits to generate Qencoder outputs; performing a signal mapping on the I encoder outputsand the Q encoder outputs to generate said I and Q waveform sequences;wherein said I and Q waveform sequences are continuous in time.
 8. Themethod of claim 7, wherein said performing the signal mapping generatesthe I waveform sequence based on the I encoder outputs and generates theQ waveform sequence based on the Q encoder outputs.
 9. The method ofclaim 7 further comprising: demultiplexing said interleaved encoded bitsto obtain said first portion and said second portion of said interleavedencoded bits.
 10. The method of claim 7, wherein said bit interleavingsaid outer encoded bits includes: performing a first bit interleaving ona first portion of said outer encoded bits to obtain said first portionof said interleaved encoded bits; performing a second bit interleavingon a second portion of said outer encoded bits to obtain said secondportion of said interleaved encoded bits.
 11. The method of claim 7,wherein said performing the modified FQPSK modulation also includes:performing quadrature modulation on quadrature carrier signals using theI and Q waveform sequences to generate an output signal.
 12. The methodof claim 7 further comprising transmitting an output signal onto achannel, wherein the output signal is determined using the I and Qwaveform sequences.
 13. A method of encoding, comprising: bitinterleaving a first portion of an input sequence of bits to producedinterleaved bits; performing a modified FQPSK modulation on saidinterleaved bits and a second portion of the input sequence of bits toproduce I and Q waveform sequences, wherein said performing the modifiedFQPSK modulation realizes a modulation with memory, wherein saidperforming the modified FQPSK modulation includes: performing a firstrecursive encoding on said interleaved bits to generate first encoderoutputs; performing a second recursive encoding on said second portionof the input sequence to generate second encoder outputs; performing asignal mapping on the first encoder outputs and the second encoderoutputs to generate said I and Q waveform sequences; wherein said I andQ waveform sequences are continuous in time.
 14. The method of claim 13,wherein said performing the signal mapping generates the I waveformsequence based on the first encoder outputs and generates the Q waveformsequence based on the second encoder outputs.
 15. The method of claim13, wherein said performing the signal mapping generates the I waveformsequence based on the second encoder outputs and generates the Qwaveform sequence based on the first encoder outputs.
 16. The method ofclaim 13, wherein said performing the modified FQPSK modulation alsoincludes: performing quadrature modulation on quadrature carrier signalsusing respectively the I and Q waveform sequences to generate an outputsignal.
 17. The method of claim 13 further comprising transmitting anoutput signal onto a channel, wherein the output signal is determinedusing the I and Q waveform sequences.
 18. An encoding system comprising:a first outer encoder configured to encode a first portion of an inputsequence of bits to produce first outer encoded bits; a second outerencoder configured to encode a second portion of the input sequence ofbits to produce second outer encoded bits; a first bit interleaverconfigured to perform bit interleaving on said first outer encoded bitsto produce first interleaved encoded bits; a second bit interleaverconfigured to perform bit interleaving on said second outer encoded bitsto produce second interleaved encoded bits; a modified FQPSK modulatorconfigured to operate on said first interleaved encoded bits and saidsecond interleaved encoded bits to produce I and Q waveform sequences,wherein said modified FQPSK modulator is configured to implement amodulation with memory, wherein said modified FQPSK modulator includes:an I-channel recursive encoder configured to encode the firstinterleaved encoded bits to generate I encoder outputs; a Q-channelrecursive encoder configured to encode the second interleaved encodedbits to generate Q encoder outputs; a signal mapper configured togenerate said I and Q waveform sequences based on the I encoder outputsand the Q encoder outputs; wherein said I and Q waveform sequences arecontinuous in time.
 19. The system of claim 18, wherein said signalmapper is configured to generate the I waveform sequence based on the Iencoder outputs and generate the Q waveform sequence based on the Qencoder outputs.
 20. The system of claim 18, wherein said first andsecond outer encoders are linear encoders each with rate less than one.21. The system of claim 18, wherein said first and second outer encodersare each repetition encoders.
 22. The system of claim 18, wherein saidmodified FQPSK modulator also includes: a quadrature modulatorconfigured to modulate quadrature carrier signals using the I and Qwaveform sequences in order to generate an output signal.
 23. The systemof claim 18, wherein the system is configured to generate an outputsignal using the I and Q waveform sequences and to transmit the outputsignal onto a channel.
 24. An encoding system comprising: an outerencoder configured to encode an input sequence of bits to produce outerencoded bits; a bit interleaver configured to bit interleave said outerencoded bits to produce interleaved encoded bits; and a modified FQPSKmodulator configured to operate on said interleaved encoded bits toproduce I and Q waveform sequences, wherein said modified FQPSKmodulator is configured to implement a modulation with memory, whereinsaid modified FQPSK modulator includes: an I-channel recursive encoderconfigured to encode a first portion of said interleaved encoded bits togenerate I encoder outputs; a Q-channel recursive encoder configured toencode a second portion of said interleaved encoded bits to generate Qencoder outputs; a signal mapper configured to generate said I and Qwaveform sequences based on the I encoder outputs and the Q encoderoutputs; wherein said I and Q waveform sequences are continuous in time.25. The system of claim 24, wherein the signal mapper is configured togenerate the I waveform sequence based on the I encoder outputs andgenerate the Q waveform sequence based on the Q encoder outputs.
 26. Thesystem of claim 24 further comprising a demultiplexer configured todemultiplex said interleaved encoded bits to obtain said first portionand said second portion of said interleaved encoded bits.
 27. The systemof claim 24, wherein said bit interleaver includes: a first bitinterleaver configured to bit interleave a first portion of said outerencoded bits to obtain said first portion of said interleaved encodedbits; a second bit interleaver configured to bit interleave a secondportion of said outer encoded bits to obtain said second portion of saidinterleaved encoded bits.
 28. The system of claim 24, wherein themodified FQPSK modulator also includes a quadrature modulator configuredto modulate quadrature carrier signals using the I and Q waveformsequences in order to generate an output signal.
 29. The system of claim24, wherein the system is configured to generate an output signal usingthe I and Q waveform sequences and to transmit the output signal onto achannel.
 30. An encoding system comprising: a bit interleaver configuredto bit interleave a first portion of an input sequence of bits toproduced interleaved bits; a modified FQPSK modulator configured tooperate on said interleaved bits and a second portion of the inputsequence of bits to produce I and Q waveform sequences, wherein saidmodified FQPSK modulator is configured to implement a modulation withmemory, wherein said modified FQPSK modulator includes: a firstrecursive encoder configured to encode said interleaved bits to generatefirst encoder outputs; a second recursive encoder configured to encodesaid second portion of the input sequence to generate second encoderoutputs; a signal mapper configured to generate said I and Q waveformsequences based on the first encoder outputs and the second encoderoutputs; wherein said I and Q waveform sequences are continuous in time.31. The system of claim 30, wherein said signal mapper is configured togenerate the I waveform sequence based on the first encoder outputs andgenerate the Q waveform sequence based on the second encoder outputs.32. The system of claim 30, wherein said signal mapper is configured togenerate the I waveform sequence based on the second encoder outputs andgenerate the Q waveform sequence based on the first encoder outputs. 33.The system of claim 30, wherein said modified FQPSK modulator alsoincludes: a quadrature modulator configured to modulate quadraturecarrier signals using the I and Q waveform sequences in order togenerate an output signal.
 34. The system of claim 30, wherein thesystem is configured to generate an output signal using the I and Qwaveform sequences and to transmit the output signal onto a channel.